This article describes the heat and mass transfer as well as the entropy generation in an unsteady double-diffusive natural convection in the presence of an external magnetic eld, Soret and Dufour eects. The analysis uses a two- dimensional skewed enclosure, where the inclined walls make a skew angle with x-axis. The governing equations in the physical domain are transformed into an orthogonal computational domain by co-ordinate transformations, and then are solved using a nite volume method based on SIMPLE algorithm. The computations are carried out in the six skewed enclosures with skew angles = 15, 30, 45, 60, 75, and 90, for a wide range of the Hartman number, Lewis number, buoyancy ratio, and Dufour coecient, while Soret coecient is kept constant at 0.25 in most of the study. Results show that the fluid flow, heat and mass transfer, as well as the entropy generation are sensible to some extent to the skew angle variation. Meanwhile, the Lewis number and buoyancy ratio have an aiding and opposing action, respectively, on suppression effect of Lorentz force against convective heat and mass transfer. It is also shown that the average entropy generation is an increasing function of Lewis number, buoyancy ratio, and Dufour coecient, while its a decreasing function of Hartman number.